A way of replacing the need to apologize or to say sorry, often by using this term to ease the tension of the situation. To make one seem not as responsible of his or her mistakes. my bad can also be an alternative term of equal meaning.

1: I had sex with your girlfriend last night.
2: What the hell?? What kind of friend are you???
1: Aw man, my fault! (or "my bad!")
2: Man it's cool, since you said my fault.